I think the best explanation would be that Blackbeard was originally schedule to be taped as a part of the S1L1 episode, but was postponed to a later date most likely due to time restrictions. Blackbeard is essentially only "Episode 1" on paper. There's no way that this episode was taped as a separate Pilot episode like past forum members use to state. This episode was most definitely taped with the other S1L5 episodes for a few reasons:
1.) The moat rejects from Blackbeard return again in the Leonardo Da Vinci episode.
2.) The production team and Kirk don't sound awkward and confused like in S1L1.
3.) The moat and temple games in Blackbeard are the same as the other S1L5 episodes.
With that being said, there's evidence that Blackbeard was not originally intended to be a S1L5 episode and was probably shoehorned into that layout at the last minute. First off, the editing in this episode is atrocious. During the moat, there's no video tape of the intern like the other S1 moats. Also, the camerawork during the temple run was shoddy and there were no credits at the end of the episode. Most likely because the episode was rushed and they didn't have time to clean it up. Also, the fact that Belshazzar and Blackbeard's temple run use the same temple layout could be the reason why the producers shoved Blackbeard into S1L5.
To answer your other question, Belshazzar was definitely the first episode produced. In one of Kirk Fogg's interviews, he states that the first ever episode took 18 hours to tape. This would make sense if it was the Belshazzar episode because they would have to postpone the temple run due to unusually long taping time. Galileo was probably the first TEMPLE RUN produced since the Belshazzar run had to be postponed. It also explains the weird awkwardness during the temple run. Also, Jennifer stated during her interview that the Mine Shaft elevator crapped out for Jammin John and they had to retape part of that run. PS: Galileo wasn't the only run where Kirk asked for the team's strategy. He also did it in some earlier S1 runs like Lost Gold Mine, Golden Ship, Lost Hammer, and Sultan Saladin.

Long story short, Blackbeard was probably originally planned to be "Episode 1" but due to time constraints they had to postpone it to a later date. But they never changed the episode number on the official roster since it was planned to be part of the first production day. This is my take on it.